The value of ba. Given: The proportions, a+1b−1=51 and a−1b+1=11.

Question

The value of ba.  Given:  The proportions, a+1b−1=51 and a−1b+1=11.

Shannon Hodgkinson · Accepted Answer

Calculation:  In order to find the value of the ratio ba, first simplify both proportions and get two equations as shown below  a+1b−1=51  a+1b−1×(b−1)=51×(b−1)  a+1=5b−5  a+1−5b=5b−5−5b  a+1−5b=5  a+1−5b−1=−5−1  a−5b=−6 (i)  On solving the second proportion, it gives  a−1b+1=11  a−1b+1×b+1=11×b+1  a−1=b+1  a−1−b=b+1−b  a−b−1=1  a−b−1+1=1+1  a−b=2 (ii)  Now solve equation (ii) for a and substitute that in equation (i) and simplify further as shown below  a−b=2  a−b+b=2+b  a=2+b  Put the value of a in equation 1  a−5b=−6  2+b−5b=−6  2−4b=−6  2−4b−2=−6−2  −4b=−8  −4b4=−84  −b=−2  b=2  ⇒a=b+2  a=2+2  a=4  Thus, the solution of the proportion is ba=24=12

Kirsten Davis · Accepted Answer

Step 1  a+1b−1=51  Multiply both sides of the equation by b−1.  a+1=(n−1)×5  Use the distributive property to multiply b−1 by 5.  a+1=5b−5  Subtract 1 from both sides.  a=5b−5−1  Subtract 1 from −5 to get −6.  a=5b−6  Step 2  a−1b+1=11  Multiply both sides of the equation by b+1.  a−1=b+1  Add 1 to both sides.  a=b+1+1  Add 1 and 1 to get 2.  a=b+2  Step 3  a−b=2  Subtract a from both sides.  −b=2−a  Divide both sides by −1.  −b−1=2−a−1  Dividing by −1 undoes the multiplication by −1.  b=2−a−1  Divide 2−a by −1.  b=a−2  Step 4  a−5b=−6S  Subtract a from both sides.  −5b=−6−a  The equation is in standard form.  −5b=−a−6  Divide both sides by −5.  −5b−5=−a−6−5  Dividing by −5 undoes the multiplication by −5.  b=−a−6−5  Divide −6−a by −5.  b=a+65

nick1337 · Accepted Answer

Step 1 a+1b−1=51 Variable b cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by b−1. a+1=(b−1)×5 Use the distributive property to multiply b−1by 5. a+1=5b-5 Swap sides so that all variable terms are on the left hand side. 5b-5=a+1 Add 5 to both sides. 5b=a+1+5 Add 1 and 5 to get 6. 5b=a+6 Divide both sides by 5. 5a5=a+65 Dividing by 5 undoes the multiplication by 5. b=a+65 Variable b cannot be equal to 1. b=a+65, b≠1 Step 2 a−1b+1=11 Variable b cannot be equal to −1 since division by zero is not defined. Multiply both sides of the equation by b+1 a−1=b+1 Swap sides so that all variable terms are on the left hand side. b+1=a−1 Subtract 1 from both sides. b=a−1−1 Subtract 1 from −1 to get −2. b=a−2 Variable b cannot be equal to −1. b=1-2 b≠-1 Step 3 a−b=2 Add b to both sides. a=2+b a−5b=−6 Add 5b to both sides. a=−6+5b

The value of \frac{b}{a}. Given: The proportions, \frac{a+1}{b-1}=\frac{5}{1}\ and\ \frac{a-1}{b+1}=\frac{1}{1}.

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